UOR Type System

IRI: https://uor.foundation/type/
Prefix: type:
Space: user
Comment: Runtime type declarations that parameterize the resolution pipeline. Types are declared by Prism applications and resolved to partitions of the ring.

This is a user-space namespace in the Apply stage of the PRISM pipeline. It provides the application layer — types, morphisms, and state that parameterize the resolution pipeline.

Learn more: Pipeline Overview · Site Bundle Semantics

Class hierarchy

Imports

https://uor.foundation/schema/
https://uor.foundation/u/
https://uor.foundation/op/

Classes

Name	Subclass Of	Disjoint With	Comment
`TypeDefinition`	`Thing`	`Constraint`, `MetricAxis`	A runtime type declaration. The root class for all UOR types. Each TypeDefinition, when resolved, produces a partition of the ring at the specified quantum level.
`PrimitiveType`	`TypeDefinition`		A primitive type defined by a fixed bit width. The carrier is the entire ring Z/(2^n)Z at the specified quantum level.
`ProductType`	`TypeDefinition`		A product (Cartesian) type formed from multiple component types. The carrier is the product of the component carriers.
`SumType`	`TypeDefinition`		A sum (disjoint union) type formed from multiple variant types. The carrier is the disjoint union of the variant carriers.
`ConstrainedType`	`TypeDefinition`		A type formed by constraining a base type with a predicate. The carrier is the subset of the base carrier satisfying the constraint.
`Constraint`	`Thing`	`TypeDefinition`, `MetricAxis`	A composable predicate that refines a type by pinning one or more site coordinates. Constraints are the parameterization mechanism for ConstrainedType.
`MetricAxis`	`Thing`	`TypeDefinition`, `Constraint`	A classification axis for constraints by their geometric effect. The three axes — vertical (ring/additive), horizontal (Hamming/bitwise), diagonal (incompatibility) — form the tri-metric coordinate system of UOR.
`CompleteType`	`TypeDefinition`		A TypeDefinition certified to satisfy the UOR completeness criterion (IT_7d): its constraint nerve N(C) has Euler characteristic χ = n and all Betti numbers β_k = 0. A CompleteType guarantees that resolution closes the site budget in O(1) — no iterative refinement is required. Completeness is attested by a cert:CompletenessCertificate linked via cert:certifiedType. This class is not addressable from a type-expr position in the term language; references from term-language positions are rejected by the resolver.
`CompletenessCandidate`	`ConstrainedType`	`CompleteType`	A ConstrainedType actively undergoing the completeness certification pipeline. Links to the resolver:ResolutionState tracking the current iteration and to the resolver:CechNerve being computed. Disjoint from CompleteType (which is already certified). This class is not addressable from a type-expr position in the term language; references from term-language positions are rejected by the resolver.
`CompletenessWitness`	`Thing`		A record of a single site-closing event: one constraint application that reduced the FreeRank deficit. Carries the applied constraint and the sitesClosed count. Forms the ordered audit trail between ConstrainedType and CompleteType.
`TypeSynthesisGoal`	`Thing`		A specification of the desired topological properties of a type to be synthesised. Carries a target Euler characteristic (targetEulerCharacteristic) and a target Betti profile (zero or more targetBettiNumber assertions). The minimal goal for O(1) resolution is: targetEulerCharacteristic = n and all targetBettiNumber = 0 — the IT_7d profile.
`TypeSynthesisResult`	`Thing`		The output of a TypeSynthesisResolver run. Contains the SynthesizedType, the realised topological signature (as a SynthesisSignature), and the SynthesisTrace recording the construction steps.
`SynthesizedType`	`ConstrainedType`		A ConstrainedType produced by the TypeSynthesisResolver. Distinguished from a hand-authored ConstrainedType by the presence of a type:synthesisResult link. May or may not be a CompleteType, depending on the synthesis goal. This class is not addressable from a type-expr position in the term language; references from term-language positions are rejected by the resolver.
`MinimalConstraintBasis`	`Thing`		The minimal set of constraints in the SynthesizedType's constraint set that is sufficient to realise the target topological signature. The minimality criterion is that removing any single member changes the realised signature.
`WittLift`	`Thing`		A ConstrainedType T' over R_{n+1} obtained by extending a ConstrainedType T over R_n. Carries a link to the base type (liftBase), the quantum level it lifts to (liftTargetLevel), and the LiftObstruction (if the lift fails to transfer completeness). A WittLift is a CompleteType iff its LiftObstruction is trivial.
`LiftObstruction`	`Thing`		The algebraic obstruction to a WittLift inheriting the completeness of its base type. Computed as the image of the spectral sequence differential d_2. If trivial (zero), the base type's completeness lifts. If non-trivial, at least one additional constraint is needed at the new quantum level.
`TwistedType`	`ConstrainedType`	`FlatType`	A ConstrainedType whose HolonomyGroup is non-trivial — at least one closed constraint path produces a non-identity dihedral element. A TwistedType may still be a CompleteType (IT_7d is a homological, not holonomic, criterion), but its resolution paths require tracking dihedral accumulation. This class is not addressable from a type-expr position in the term language; references from term-language positions are rejected by the resolver.
`FlatType`	`ConstrainedType`	`TwistedType`	A ConstrainedType whose HolonomyGroup is trivial — all closed constraint paths have identity monodromy. The constraint configuration is topologically flat: resolution is path-independent. This class is not addressable from a type-expr position in the term language; references from term-language positions are rejected by the resolver.
`SuperposedSiteState`	`TypeDefinition`		A type representing a superposition of site states where sites carry complex amplitudes rather than binary pinned/free assignments. Ontological realisation of RC_5 (Amendment 32). This class is not addressable from a type-expr position in the term language; references from term-language positions are rejected by the resolver.
`ForbiddenSignature`	`Thing`		A topological signature (χ, β_k) that is formally impossible to achieve for any ConstrainedType. Witnessed by an ImpossibilityWitness in proof/.
`CollapsedSiteState`	`Thing`		A site state that has undergone projective collapse from a SuperposedSiteState to a definitive classical value. Topologically equivalent to a classically pinned site (QM_2).
`LiftChain`	`Thing`		An ordered composition of WittLift steps from liftSourceLevel (Q_j) to liftTargetLevel (Q_k) for any j < k. The canonical object certifying type completeness at arbitrary Q_k.
`ObstructionChain`	`Thing`		The complete ordered sequence of LiftObstruction records encountered and resolved along a LiftChain. An empty ObstructionChain means the tower is flat.
`ModuliSpace`	`Thing`		The space of all CompleteTypes over R_n at a given quantum level.
`HolonomyStratum`	`Thing`		A stratum indexed by a conjugacy class of subgroups of D_{2^n}.
`DeformationFamily`	`Thing`		A one-parameter family of constraint configurations parameterizing a path.
`VersalDeformation`	`Thing`		The versal deformation of a CompleteType T.
`ModuliTowerMap`	`Thing`		The map induced by WittLift from one moduli space to the next.
`GaloisConnection`	`Thing`		The adjunction between the type lattice and the site lattice. The upper adjoint is type closure; the lower adjoint is site interior. σ = lower adjoint evaluation; r = complement of upper adjoint image.
`TypeInclusion`	`Transform`		A morphism T₁ → T₂ witnessing that T₁ is a subtype of T₂: the constraint set of T₁ is a superset of the constraint set of T₂.
`VarianceAnnotation`	`Thing`		The variance of a structural type position under operad composition. One of Covariant, Contravariant, Invariant, or Bivariant.
`SubtypingLattice`	`Thing`		The partial order on types induced by TypeInclusion. The top element is PrimitiveType (no constraints); the bottom elements are CompleteTypes (all sites pinned).
`ConstraintDefaults`	`Thing`		Declarative defaults for type:Constraint subclasses, consumed by #[derive(ConstrainedType)] at macro-crate build time.
`BoundConstraint`	`Constraint`		Parametric constraint carrier consumed by the codegen to emit `BoundConstraint<O: Observable, B: BoundShape>` in the Rust foundation. The (observable, bound_shape) pair picks the predicate form; the typed datatype properties (modulus, residue, hammingBound, ...) carry the parameters for that specific kind. Replaces the seven v0.2.1 enumerated Constraint subclasses with a parametric form; the legacy names survive as Rust type aliases (ResidueConstraint, HammingConstraint, ...).
`BoundShape`	`Thing`		The predicate form a BoundConstraint imposes on its bound observable. Closed enumeration with exactly six named individuals (EqualBound, LessEqBound, GreaterEqBound, RangeContainBound, ResidueClassBound, AffineEqualBound). Adding a new bound shape is an ontology+grammar+codegen edit on the same protocol as adding a Witt level.
`Conjunction`	`Constraint`		A conjunction of BoundConstraint instances. The conjuncts property is ordered. Replaces the v0.2.1 CompositeConstraint enumeration; the legacy name survives as a Rust type alias (CompositeConstraint<const N: usize> = Conjunction<N>).

Properties

Name	Kind	Functional	Domain	Range	Comment
`bitWidth`	Datatype	true	`PrimitiveType`	`positiveInteger`	The bit width of a primitive type (the quantum level n). The carrier is Z/(2^n)Z.
`component`	Object	false	`ProductType`	`TypeDefinition`	A component type in a product type.
`variant`	Object	false	`SumType`	`TypeDefinition`	A variant type in a sum type. Ordering contract: variants are returned in canonical content-fingerprint order (ascending), matching the canonicalization used by coproduct_shape! and the content-address hashing pipeline, so introspection via variant() and the algebra_id derived from the same type agree on which variant is 'left' and which is 'right'. Author-order is not preserved.
`tagSite`	Object	true	`SumType`	`TagSite`	The tag site distinguishing variants of this sum type at runtime (ST_6). Stored at the physical layout position max(SITE_COUNT(A), SITE_COUNT(B)) so the tag cannot collide with any inherited bookkeeping site when either operand is itself a coproduct.
`baseType`	Object	true	`ConstrainedType`	`TypeDefinition`	The base type that a constrained type restricts.
`contentAddress`	Object	true	`TypeDefinition`	`Element`	The content-derived address of this type definition, uniquely identifying the type in the UOR address space.
`hasConstraint`	Object	false	`ConstrainedType`	`Constraint`	A typed constraint object applied to this constrained type. Replaces the deprecated string-based type:constraint property.
`modulus`	Datatype	true	`BoundConstraint`	`positiveInteger`	The modulus m of a residue constraint: x ≡ r (mod m).
`residue`	Datatype	true	`BoundConstraint`	`nonNegativeInteger`	The residue value r of a residue constraint: x ≡ r (mod m).
`carryPattern`	Object	true	`BoundConstraint`	`Datum`	The carry propagation pattern of a carry constraint, expressed as a Datum at the appropriate quantum level.
`minDepth`	Datatype	true	`BoundConstraint`	`nonNegativeInteger`	The minimum factorization depth required by a depth constraint.
`maxDepth`	Datatype	true	`BoundConstraint`	`nonNegativeInteger`	The maximum factorization depth allowed by a depth constraint.
`composedFrom`	Object	false	`Conjunction`	`Constraint`	A component constraint of this composite constraint.
`hammingBound`	Datatype	true	`BoundConstraint`	`nonNegativeInteger`	Upper bound on the Hamming weight of the Datum.
`siteIndex`	Datatype	true	`BoundConstraint`	`nonNegativeInteger`	Zero-based index of the pinned site coordinate.
`siteValue`	Object	true	`BoundConstraint`	`Datum`	The value the pinned site coordinate must equal (a Datum in the set {0, 1}).
`affineOffset`	Object	true	`BoundConstraint`	`Datum`	Constant offset defining the affine subspace.
`affineGenerator`	Object	false	`BoundConstraint`	`Datum`	A generator of the affine subspace. Non-functional: multiple generators span the subspace.
`metricAxis`	Object	true	`Constraint`	`MetricAxis`	The metric axis along which this constraint operates: vertical (ring), horizontal (Hamming), or diagonal (incompatibility).
`pinsSites`	Object	false	`Constraint`	`SiteIndex`	A site coordinate that this constraint pins when applied.
`affectsAxis`	Object	false	`Operation`	`MetricAxis`	The metric axis that this operation affects. Replaces the string-valued type:axisSignature property with a typed reference to MetricAxis individuals. Non-functional: an operation may affect multiple axes.
`crossingCost`	Datatype	true	`Constraint`	`nonNegativeInteger`	The cost of applying this constraint in terms of axis crossings: the number of metric boundaries that must be traversed.
`completenessCandidate`	Object	false	`CompletenessCandidate`	`ConstrainedType`	The ConstrainedType being evaluated for completeness by this CompletenessCandidate.
`candidateNerve`	Object	true	`CompletenessCandidate`	`CechNerve`	The constraint nerve being computed for this candidate. The CompletenessResolver reads χ(N(C)) from this nerve at each iteration via resolver:nerveEulerCharacteristic.
`witnessConstraint`	Object	true	`CompletenessWitness`	`Constraint`	The constraint applied in this witness step.
`sitesClosed`	Datatype	true	`CompletenessWitness`	`nonNegativeInteger`	Number of sites closed by this witness step.
`targetEulerCharacteristic`	Datatype	true	`TypeSynthesisGoal`	`integer`	The target χ(N(C)) value. For O(1) resolution: set equal to n (the quantum level).
`targetBettiNumber`	Datatype	false	`TypeSynthesisGoal`	`nonNegativeInteger`	Non-functional. Each assertion specifies a target Betti number value for a given homological degree. Multiple assertions permitted, one per degree.
`synthesisResult`	Object	true	`SynthesizedType`	`TypeSynthesisResult`	Links a SynthesizedType back to the synthesis run that produced it.
`basisConstraint`	Object	false	`MinimalConstraintBasis`	`Constraint`	Non-functional. One assertion per constraint in the minimal basis.
`basisSize`	Datatype	true	`MinimalConstraintBasis`	`nonNegativeInteger`	The cardinality of the minimal basis. The theoretical lower bound is n (one constraint per site).
`liftBase`	Object	true	`WittLift`	`ConstrainedType`	The base type being lifted to the next quantum level.
`liftTargetLevel`	Object	true	`WittLift`	`WittLevel`	The quantum level this lift targets.
`liftObstruction`	Object	true	`WittLift`	`LiftObstruction`	The LiftObstruction for this lift. Trivial (zero class) iff the lift inherits completeness.
`obstructionTrivial`	Datatype	true	`LiftObstruction`	`boolean`	True iff the obstruction class is zero — the base type's completeness transfers to the lifted quantum level without additional constraints.
`obstructionSite`	Object	true	`LiftObstruction`	`SiteIndex`	The site at the new quantum level where the obstruction is located. Ranges over the new bit position introduced at Q_{n+1}.
`holonomyGroup`	Object	true	`ConstrainedType`	`HolonomyGroup`	The HolonomyGroup of this type. Computed by the MonodromyResolver.
`monodromyClass`	Object	true	`ConstrainedType`	`MonodromyClass`	The MonodromyClass classifying this type as flat or twisted.
`amplitude`	Datatype	true	`SuperposedSiteState`	`decimal`	The amplitude coefficient for this superposed site state.
`targetForbidden`	Datatype	true	`TypeSynthesisGoal`	`boolean`	Whether the target signature of this TypeSynthesisGoal is a ForbiddenSignature. If true, synthesis is provably impossible.
`collapsedFrom`	Object	true	`CollapsedSiteState`	`SuperposedSiteState`	The SuperposedSiteState from which this CollapsedSiteState was produced by projective measurement.
`survivingAmplitude`	Datatype	true	`CollapsedSiteState`	`decimal`	The amplitude of the surviving branch after projective collapse. \|α\|² is the probability of this outcome under the Born rule.
`normalizationVerified`	Datatype	true	`SuperposedSiteState`	`boolean`	Whether the amplitude vector of this SuperposedSiteState satisfies the normalization condition Σ\|αᵢ\|² = 1 (QM_5). Set by the SuperpositionResolver after verification.
`holonomyClassified`	Datatype	true	`ConstrainedType`	`boolean`	Whether this ConstrainedType has been classified as FlatType or TwistedType by the MonodromyResolver. The MN_8 identity guarantees this is a bivalent classification: holonomyClassified(T) iff isFlatType(T) xor isTwistedType(T).
`liftSourceLevel`	Object	true	`LiftChain`	`WittLevel`	The quantum level at the base of the chain.
`chainLength`	Datatype	true	`LiftChain`	`nonNegativeInteger`	The number of WittLift steps in the chain (k - j).
`chainStep`	Object	false	`LiftChain`	`WittLift`	A WittLift step in this chain. Non-functional: one per step.
`chainObstructionProfile`	Object	true	`LiftChain`	`ObstructionChain`	The full obstruction history of this chain.
`resolvedBasisSize`	Datatype	true	`LiftChain`	`nonNegativeInteger`	The basis size of the CompleteType at the chain target level.
`obstructionAt`	Object	false	`ObstructionChain`	`LiftObstruction`	A non-trivial LiftObstruction in this chain. Non-functional.
`obstructionCount`	Datatype	true	`ObstructionChain`	`nonNegativeInteger`	Total number of non-trivial LiftObstruction records.
`isFlat`	Datatype	true	`ObstructionChain`	`boolean`	True iff obstructionCount = 0 (flat tower).
`moduliWittLevel`	Object	true	`ModuliSpace`	`WittLevel`	The quantum level at which this moduli space is defined.
`moduliPoint`	Object	false	`ModuliSpace`	`CompleteType`	A CompleteType that is a point of this moduli space.
`moduliDimension`	Datatype	true	`ModuliSpace`	`nonNegativeInteger`	The dimension of this moduli space.
`stratumHolonomyClass`	Object	true	`HolonomyStratum`	`MonodromyClass`	The MonodromyClass indexing this stratum.
`stratumCodimension`	Datatype	true	`HolonomyStratum`	`nonNegativeInteger`	The codimension of this stratum within the moduli space.
`stratumModuli`	Object	true	`HolonomyStratum`	`ModuliSpace`	The moduli space containing this stratum.
`familyParameter`	Object	false	`DeformationFamily`	`CompleteType`	A CompleteType along the deformation path.
`familyPreservesCompleteness`	Datatype	true	`DeformationFamily`	`boolean`	Whether every member of this deformation family remains a CompleteType.
`versalBase`	Object	true	`VersalDeformation`	`CompleteType`	The CompleteType at the base of this versal deformation.
`versalDimension`	Datatype	true	`VersalDeformation`	`nonNegativeInteger`	The dimension of the versal deformation space.
`towerMapSource`	Object	true	`ModuliTowerMap`	`ModuliSpace`	The source moduli space of this tower map.
`upperAdjoint`	Object	true	`GaloisConnection`	`TermExpression`	The upper adjoint (type closure) of the Galois connection, expressed as a symbolic formula string.
`lowerAdjoint`	Object	true	`GaloisConnection`	`TermExpression`	The lower adjoint (site interior) of the Galois connection, expressed as a symbolic formula string.
`fixpointCondition`	Object	true	`GaloisConnection`	`TermExpression`	The fixpoint condition for the Galois connection: when upper(lower(T)) = T, the type is complete.
`refinementDirection`	Datatype	true	`GaloisConnection`	`nonNegativeInteger`	Description of the refinement direction: ascending in type lattice corresponds to descending in site freedom.
`structuralSiteCount`	Annotation	true	`—`	`string`	Formula or description of the site count for a structural type individual.
`structuralGrounding`	Annotation	true	`—`	`string`	Description of the grounding rule that maps values of this structural type onto the UOR ring.
`structuralConstraint`	Annotation	true	`—`	`string`	Description of the constraint characterizing this structural type, if applicable.
`galoisClosureProperty`	Object	true	`GaloisConnection`	`TermExpression`	The closure property of a Galois connection.
`galoisInteriorProperty`	Object	true	`GaloisConnection`	`TermExpression`	The interior property of a Galois connection.
`groundingMapRef`	Object	true	`—`	`GroundingMap`	Reference to the grounding map used for this type.
`compositionLaw`	Object	true	`—`	`TermExpression`	The algebraic composition law governing this type.
`siteOrderingConstraint`	Object	true	`—`	`TermExpression`	Constraint on the ordering of sites for this type.
`backboneThreshold`	Datatype	true	`—`	`nonNegativeInteger`	The threshold for backbone inclusion in the type lattice.
`permutationGroup`	Object	true	`—`	`Group`	The permutation group acting on sites of this type.
`acyclicityWitness`	Datatype	true	`—`	`boolean`	Witness certifying acyclicity of the type dependency graph.
`connectivityWitness`	Datatype	true	`—`	`boolean`	Witness certifying connectivity of the type graph.
`schemaConstraint`	Object	true	`—`	`TermExpression`	Constraint imposed by the schema on this type.
`alphabetSize`	Annotation	true	`—`	`nonNegativeInteger`	The size of the alphabet for symbol-based types.
`quantizationRange`	Object	true	`—`	`TermExpression`	The range specification for quantized types.
`elementTypeRef`	Object	true	`—`	`TypeDefinition`	Reference to the element type within a composite type.
`inclusionSource`	Object	true	`TypeInclusion`	`ConstrainedType`	The subtype (more constraints).
`inclusionTarget`	Object	true	`TypeInclusion`	`ConstrainedType`	The supertype (fewer constraints).
`positionVariance`	Object	true	`StructuralOperad`	`VarianceAnnotation`	The variance of each operand position.
`inclusionWitness`	Datatype	true	`TypeInclusion`	`boolean`	True iff constraints(source) ⊇ constraints(target). Computed, not asserted.
`latticeDepth`	Datatype	true	`SubtypingLattice`	`nonNegativeInteger`	Maximum chain length from PrimitiveType (top) to any CompleteType (bottom). Equals the site budget n at quantum level Q_k.
`defaultValue`	Datatype	true	`ConstraintDefaults`	`integer`	Default integer value for the named constraint default.
`boundObservable`	Object	true	`BoundConstraint`	`Observable`	The observable:Observable whose values this BoundConstraint bounds. Picks which datum projection is being constrained.
`boundShape`	Object	true	`BoundConstraint`	`BoundShape`	The predicate form this BoundConstraint imposes on its bound observable. Closed enumeration with exactly six named individuals (EqualBound, LessEqBound, GreaterEqBound, RangeContainBound, ResidueClassBound, AffineEqualBound).
`boundArguments`	Datatype	true	`BoundConstraint`	`string`	The BoundConstraint's parameters in canonical string form (e.g., 'modulus=256;residue=255' for a residue class bound). Non-functional — the string-form encoding is the canonical serialization; typed accessors on the Rust side unpack it via the per-type-alias constructors.
`conjuncts`	Object	false	`Conjunction`	`BoundConstraint`	An ordered list of BoundConstraint individuals that this Conjunction composes. Non-functional — multiple conjuncts span the conjunction.

Named Individuals

Name	Type	Comment
`verticalAxis`	`MetricAxis`	The vertical (ring/additive) metric axis. Constraints on this axis operate through ring arithmetic: residue classes, divisibility, and additive structure.
`horizontalAxis`	`MetricAxis`	The horizontal (Hamming/bitwise) metric axis. Constraints on this axis operate through bitwise structure: carry patterns, bit positions, and Hamming distance.
`diagonalAxis`	`MetricAxis`	The diagonal (incompatibility) metric axis. Constraints on this axis measure the gap between ring and Hamming metrics — the curvature of UOR geometry.
`ScalarType`	`PrimitiveType`	A single value from an ordered domain. siteCount = n (quantization bits).
`structuralSiteCount`: n (quantization bits) `structuralGrounding`: quantize(value, range, bits) produces ring element where d_R reflects value proximity
`SymbolType`	`PrimitiveType`	A value from a finite unordered set. siteCount = ceil(log2(\|alphabet\|)).
`structuralSiteCount`: ceil(log2(\|alphabet\|)) `structuralGrounding`: argmin_{encoding} sum d_delta over observed pairs (CY_5)
`SequenceType`	`ProductType`	An ordered list of elements with backbone constraint. The free monoid on the element type.
`structuralSiteCount`: sum of element site counts `structuralGrounding`: free monoid on element type, backbone constraint `structuralConstraint`: backbone ordering: elements indexed by position
`TupleType`	`ProductType`	A fixed collection of named fields.
`structuralSiteCount`: sum of field site counts `structuralGrounding`: site ordering follows CY_6 (optimal site ordering)
`GraphType`	`ConstrainedType`	Nodes with edge constraints. Constraint nerve = graph topology.
`structuralSiteCount`: sum of node site counts + edge overhead `structuralGrounding`: constraint nerve = graph nerve, beta_k equality `structuralConstraint`: edge constraints: adjacency preserved under grounding
`SetType`	`ConstrainedType`	Unordered collection. d_delta is permutation-invariant.
`structuralSiteCount`: sum of element site counts `structuralGrounding`: d_delta invariant under element permutation, D_{2n} symmetry `structuralConstraint`: permutation invariance: encoding is order-independent
`TreeType`	`ConstrainedType`	Hierarchical structure. beta_1=0 (acyclic), beta_0=1 (connected).
`structuralSiteCount`: sum of node site counts `structuralGrounding`: parent-child encoding with acyclicity constraint `structuralConstraint`: beta_1=0 (acyclic), beta_0=1 (connected)
`TableType`	`ProductType`	Collection of tuples sharing a schema = Sequence(Tuple(S)). Functorial decomposition.
`structuralSiteCount`: row_count * tuple_site_count `structuralGrounding`: Sequence(Tuple(S)), functorial decomposition `structuralConstraint`: shared schema: all rows conform to tuple type S
`Covariant`	`VarianceAnnotation`	The structural position preserves TypeInclusion: if T₁ ≤ T₂, then F(T₁) ≤ F(T₂).
`enumVariant`: `Covariant`
`Contravariant`	`VarianceAnnotation`	The structural position reverses TypeInclusion: if T₁ ≤ T₂, then F(T₂) ≤ F(T₁).
`enumVariant`: `Contravariant`
`Invariant`	`VarianceAnnotation`	The structural position requires exact type equality: F(T₁) ≤ F(T₂) only if T₁ = T₂.
`enumVariant`: `Invariant`
`Bivariant`	`VarianceAnnotation`	The structural position ignores the type parameter: F(T₁) ≤ F(T₂) for all T₁, T₂.
`enumVariant`: `Bivariant`
`EitherType`	`SumType`	The canonical binary disjoint union type whose carrier is L + R.
`OptionType`	`SumType`	The canonical A + Unit idiom for optional values.
`ResidueDefaultModulus`	`ConstraintDefaults`	Default modulus for ResidueConstraint when the #[uor(residue = X)] attribute omits the explicit modulus. 256 matches the v0.2.1 reference ring Z/(2^8)Z.
`defaultValue`: 256
`EqualBound`	`BoundShape`	Predicate form: `observable(datum) == target`. Used by BoundConstraint instances asserting strict equality of a datum's observable projection to a target value.
`LessEqBound`	`BoundShape`	Predicate form: `observable(datum) <= bound`. Used by hamming, depth, carry, and site-rank bound constraints.
`GreaterEqBound`	`BoundShape`	Predicate form: `observable(datum) >= bound`.
`RangeContainBound`	`BoundShape`	Predicate form: `lo <= observable(datum) <= hi`. The datum's observable projection must lie within the inclusive range `[lo, hi]`.
`ResidueClassBound`	`BoundShape`	Predicate form: `observable(datum) ≡ residue (mod modulus)`. Used by BoundConstraint instances asserting residue-class membership.
`AffineEqualBound`	`BoundShape`	Predicate form: `observable(datum) == offset + Σ αᵢ·generatorᵢ`. The datum's observable projection must equal an affine combination of the BoundConstraint's affine generators.
`LexicographicLessEqBound`	`BoundShape`	Predicate form: `observable(datum) <= bound` over byte-sequence-valued observables under canonical big-endian unsigned ordering. Fixed-length: lexicographic byte-wise comparison. Variable-length: lexicographic with shorter-prefix-rule (the shorter sequence is less than the longer when bytes match through the shorter's length). Wiki ADR-040 + ADR-038: this is the BoundShape primitive for byte-sequence-valued AxisProjectionObservable instances (e.g. axis-realized hash projections) — LessEqBound is the integer-valued primitive (HammingMetric, DerivationDepthObservable, etc.).
`residueConstraintKind`	`BoundConstraint`	Parametric replacement for the v0.2.1 ResidueConstraint class: (observable:ValueModObservable, type:ResidueClassBound). The Rust foundation exposes this kind via the `ResidueConstraint` type alias with `pub const fn new(modulus, residue)`.
`boundObservable`: `ValueModObservable` `boundShape`: `ResidueClassBound` `boundArguments`: modulus=256;residue=0
`hammingConstraintKind`	`BoundConstraint`	Parametric replacement for the v0.2.1 HammingConstraint class: (observable:HammingMetric, type:LessEqBound). The Rust foundation exposes this kind via the `HammingConstraint` type alias with `pub const fn new(bound)`.
`boundObservable`: `HammingMetric` `boundShape`: `LessEqBound` `boundArguments`: bound=0
`depthConstraintKind`	`BoundConstraint`	Parametric replacement for the v0.2.1 DepthConstraint class: (derivation:DerivationDepthObservable, type:LessEqBound).
`boundObservable`: `DerivationDepthObservable` `boundShape`: `LessEqBound` `boundArguments`: min_depth=0;max_depth=0
`carryConstraintKind`	`BoundConstraint`	Parametric replacement for the v0.2.1 CarryConstraint class: (carry:CarryDepthObservable, type:LessEqBound).
`boundObservable`: `CarryDepthObservable` `boundShape`: `LessEqBound` `boundArguments`: bound=0
`siteConstraintKind`	`BoundConstraint`	Parametric replacement for the v0.2.1 SiteConstraint class: (partition:FreeRankObservable, type:LessEqBound).
`boundObservable`: `FreeRankObservable` `boundShape`: `LessEqBound` `boundArguments`: site_index=0
`affineConstraintKind`	`BoundConstraint`	Parametric replacement for the v0.2.1 AffineConstraint class: (observable:ValueModObservable, type:AffineEqualBound).
`boundObservable`: `ValueModObservable` `boundShape`: `AffineEqualBound` `boundArguments`: offset=0

UOR Type System

Imports

Classes

Properties

Named Individuals

Related Concepts